A Set-up Model for A Set-up Model for Tandem Cold Rolling Tandem Cold Rolling

Mills Mills (October 24, 2001)(October 24, 2001)

byby

N. Venkata N. Venkata

G. SuryanarayanaG. Suryanarayana

Paper Presented By:Paper Presented By:

Nathan ZollingerNathan Zollinger

September 13, 2004September 13, 2004

ReferencesReferences

BackgroundBackground

“The demand for rolled products has increased tremendously in automobile, aircraft, food and other industries.With the increase in the demand for rolled products, the focus has shifted towards the tandem rolling mills which can operate at very high speeds and in which large reductions can be achieved with relatively close tolerance on flatness and thickness” (269).

The ProblemThe Problem

=

So how can I make my rolling So how can I make my rolling operations more operations more

profitable?profitable?

Solutions?Solutions?

=1. Modernize/enhance rolling mill setup

2. Explore/implement innovative rolling designs/processes

3. Specialize in market niche

4. Other?ENHANCE REDUCTION SCHEDULE!

Reduction ScheduleA A reduction schedulereduction schedule assigns % thickness assigns % thickness reductions for a given amount of roll passes. For a reductions for a given amount of roll passes. For a series of rollers, a tandem setup, each roller will be series of rollers, a tandem setup, each roller will be assigned a reduction percentage.assigned a reduction percentage.

In rolling, a strip is rolled continuously through 4-7 In rolling, a strip is rolled continuously through 4-7 individual mills (tandem setup) at high speed with individual mills (tandem setup) at high speed with no stopping between mills. This requires much no stopping between mills. This requires much investment into efficient calculations and controls to investment into efficient calculations and controls to minimize rolling costs. minimize rolling costs.

Perhaps there exists an optimum reduction Perhaps there exists an optimum reduction schedule that will lower energy consumption, i.e., schedule that will lower energy consumption, i.e., minimize rolling costs.minimize rolling costs.

Reduction ScheduleHomework Problem 19.6–constant % reductionHomework Problem 19.6–constant % reduction

A constant reduction schedule is also known as geometric

Thickness Profile (constant or geometric % reduction)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8

Stand (Roll Number)

Th

ickn

ess

(in

.)

Reduction Schedule

Thickness Profile (harmonic % reduction)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8

Stand (Roller Number)

Th

ickn

ess

(in

.)

What about Harmonic, Linear, & Quadratic Schedules?What about Harmonic, Linear, & Quadratic Schedules?

Thickness Profile (linear % reduction)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8

Stand (Roller Number)

Th

ick

ne

ss

(i

n.)

The paperN. Venkata and G. Suryanarayana seek to establish an N. Venkata and G. Suryanarayana seek to establish an optimum tandem roller reduction schedule that will result optimum tandem roller reduction schedule that will result in better energy efficiency during rolling processes.in better energy efficiency during rolling processes.

How? Utilize understanding of deformation mechanics to How? Utilize understanding of deformation mechanics to model power requirements for a few reduction schedules.model power requirements for a few reduction schedules.

Math ModelMath Model

Utilize one-dimensional mathematical Utilize one-dimensional mathematical models models

• Less computational time than Less computational time than other methodsother methods• Predicts Roll Force, Roll Torque, Predicts Roll Force, Roll Torque, and Pressure distributions with and Pressure distributions with reasonable accuracyreasonable accuracy

Axial Equilibrium EquationAxial Equilibrium Equation

Math ModelMath ModelP

O

W

E

R

1. Axial Equilibrium Equation

2. Rearrange and solve for σ using the Runge Kutta Method

3. Use σ to find normal pressure

Math ModelMath ModelASSUMPTIONSASSUMPTIONS Material is isotropic, incompressible, and yields according to the Von Material is isotropic, incompressible, and yields according to the Von Mises Criterion*Mises Criterion* Rolls are rigid and the coefficient of friction is constant over the roll-work Rolls are rigid and the coefficient of friction is constant over the roll-work interfaceinterface Deformation is homogenous and takes place under isothermal conditionsDeformation is homogenous and takes place under isothermal conditions

CONSTRAINTS CONSTRAINTS Minimum Minimum μμ required at the maximum possible reduction (required at the maximum possible reduction (ΔΔhhmaxmax = = μμ22R) R) is:is:

*The von Mises Criterion (1913) is often used to estimate the yield of ductile materials. The von Mises criterion states that failure occurs when the energy of distortion reaches the same energy

for yield/failure in uniaxial tension.

ResultsResults

Test results run for various schedules were matched against a previously suggested reduction schedule (Roberts); the harmonic arrangement yielded the least power consumption

ResultsResults

ConclusionConclusion

Distributing the strip thicknesses in harmonic series will minimize power consumed and create savings in tandem mill operations!